The tie was virtually already settled after the first leg as the Reds romped to a 5-0 win in Portugal last month.
Jurgen Klopp's charges enjoyed most of the possession in the early stages of the half, although they struggled to carve out clear-cut chances.
Sadio Mane, who netted a hat-trick in the first leg, did go close on 18 minutes with an acrobatic strike that narrowly sailed over the bar.
The Reds upped the tempo after 30 minutes and went close on a couple occasions, with James Milner rattling the post.
Porto, meanwhile, struggled to fashion any opportunities in the final third as Reds shot-stopper Loris Karius enjoyed a quiet opening 45 minutes.
Karius was called upon seven minutes into the second half as he produced a fine low save to deny Abdul Majeed Waris.
Jurgen Klopp introduced Danny Ings for Roberto Firmino on 62 minutes and the former nearly opened the scoring five minutes after his introduction but his header was saved by Iker Casillas.
The game livened up in the final 15 minutes as both sides pushed for a winning goal, although they were both let down by their finishing.
In the end, 0-0 was how the second leg ended, although the Reds are through to the last-eight thanks to their emphatic first-leg win.